## Optimization of the shape of Gaussian beams of a fixed length

**Ludek Klimes**
### Summary

The procedure of choosing the shape of Gaussian beams
in order to minimize a given object function of a certain kind
is proposed.
The general form of the object function enables both the average
square of the quadratic variation of the phase and the average
square of the beamwidth to be minimized along the central ray.
The error of the transformation of the Gaussian beams
at the structural interfaces may also be taken into account.
Most of the hitherto published suggestions of how to
choose the shape of Gaussian beams are special cases of the described
procedure.
The aim of this paper is not to propose the object
function to be minimized, but only to describe the minimization
of a given object function. The minimization assumes the a priori
known lengths of the central rays
of the Gaussian beams (i.e. the lengths of the beams
are not free parameters in the minimization procedure).

### Whole paper

The
image of the reprint in GIF 150dpi (3624 kB !)
is designed for an instant screen preview.

The scanned
image of the reprint in PDF 300dpi (698 kB)
is designed for printing.

Stud. geophys. geod., **33** (1989), 146-163.

SW3D
- main page of consortium ** Seismic Waves in Complex 3-D Structures **.